Methods to obtain discrete analogs of continuous distributions have been widely applied in recent years. In general, the discretization process provides probability mass functions that can be competitive with traditional models used in the analysis of count data. The discretization procedure also avoids the use of continuous distribution to model strictly discrete data. In this paper, we propose two discrete analogs for the quasi xgamma distribution as alternatives to model under- and overdispersed datasets. The methods of infinite series and survival function have been considered to derive the models and, despite the difference between the methods, the resulting distributions are interchangeable. Several statistical properties of the proposed models have been derived. The maximum likelihood theory has been considered for estimation and asymptotic inference concerns. An intensive simulation study has been carried out in order to evaluate the main properties of the maximum likelihood estimators. The usefulness of the proposed models has been assessed by using two real datasets provided by literature. A general comparison of the proposed models with some well-known discrete distributions has been provided.

中文翻译：

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离散拟Xgamma分布

近年来，获得连续分布的离散类似物的方法已被广泛应用。通常，离散化过程提供的概率质量函数可以与计数数据分析中使用的传统模型竞争。离散化过程还避免了使用连续分布对严格离散的数据进行建模。在本文中，我们为准xgamma分布提出了两个离散的类似物，作为对欠分散和过分散数据集进行建模的替代方法。已经考虑了无穷级数和生存函数的方法来推导模型，尽管方法之间存在差异，但所得分布是可互换的。推导模型的几个统计特性已经得到。已考虑将最大似然理论用于估计和渐近推理问题。为了评估最大似然估计器的主要属性，已经进行了深入的模拟研究。通过使用文献提供的两个真实数据集评估了提出的模型的有效性。已对提出的模型与一些众所周知的离散分布进行了一般比较。